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Poonen, Bjorn

Rational Points on Varieties / Bjorn Poonen - rovidence, Rhode Island : American Mathematical Society, 2017 - xv, 337 pages : illustrations ; 27 cm. - Graduate studies in mathematics, v. 186. .

Preface --
Fields --
Varieties over arbitrary fields --
Properties of morphisms --
Faithfully flat descent --
Algebraic groups --
Êtale and fppf cohomology --
The Weil conjectures --
Cohomological obstructions to rational points --
Surfaces --
Appendix A. Universes --
Appendix B. Other kinds of fields --
Appendix C. Properties under base extension.

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one.

ISBN: 9781470454753

Subjects--Topical Terms:
Mathematics
Geometry
Rational points Geometry
Algebraic varieties.
Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points.
Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Varieties over global fields.

Dewey Class. No.: 516.35 POO